Two parallel single phase rectifiers by using single phase to three phase induction motor

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 441
TWO PARALLEL SINGLE PHASE RECTIFIERS BY USING SINGLE
PHASE TO THREE PHASE INDUCTION MOTOR
Vaddi Ramesh1
, P Anjappa2
, P.Dhanamjaya3
1
PH.D Student, Department of Electrical and Electronics Engineering, KL University, Guntur (AP) India)
2
HOD & Associate professor, 3
Assistant professor, Department of EEE, Golden valley integrated campus, Madanapalli,
A.P, India, rameshvaddi6013@gmail.com, anji_abhi@yahoo.co.in, dhanam302@gmail.com
Abstract
A single-phase to three-phase drive system composed of two parallel single-phase rectifiers, a three-phase inverter and an induction
motor was proposed. The system combines two parallel rectifiers without the use of transformers. The system model and the control
strategy, including the PWM technique, have been developed.
The complete comparison between the proposed and standard configurations has been carried out in this paper. Compared to the
conventional topology, the proposed system permits to reduce the rectifier switch currents, the THD of the grid current with same
switching frequency or the switching frequency with same THD of the grid current and to increase the fault tolerance characteristics.
In addition, the losses of the proposed system may be lower than that of the conventional counterpart.
The initial investment of the proposed system (due to high number of semiconductor devices) cannot be considered a drawback,
especially considering the scenario where the cited advantages justify such initial investment. The experimental results have shown
that the system is controlled properly, even with transient and occurrence of fault
----------------------------------------------------------------------***-----------------------------------------------------------------------
1. INTRODUCTION
Several solutions have been proposed when the objective is to
supply a three-phase motor from single-phase ac mains. It is
quite common to have only a single phase power grid in
residential, commercial, manufacturing, and mainly in rural
areas, while the adjustable speed drives may request a three-
phase power grid. Single-phase to three-phase ac–dc–ac
conversion usually employs a full-bridge topology, which
implies in ten power switches. This converter is denoted here
as conventional topology. Parallel converters have been used
to improve the power capability, reliability, efficiency, and
redundancy. Parallel converter techniques can be employed to
improve the performance of active power filters,
uninterruptible power supplies (UPS), fault tolerance of
doubly fed induction generators, and three-phase drives.
Usually the operation of converters in parallel requires a
transformer for isolation. However, weight, size, and cost
associated with the transformer may make such a solution
undesirable. When an isolation transformer is not used, the
reduction of circulating currents among different converter
stages is an important objective in the system design.
In this paper, a single-phase to three-phase drive system
composed of two parallel single-phase rectifiers and a three-
phase inverter is proposed. The proposed system is conceived
to operate where the single-phase utility grid is the unique
option available. Compared to the conventional topology, the
proposed system permits to reduce the rectifier switch
currents, the total harmonic distortion (THD) of the grid
current with same switching frequency or the switching
frequency with same THD of the grid current, and to increase
the fault tolerance characteristics. In addition, the losses of the
proposed system may be lower than that of the conventional
counterpart. The aforementioned benefits justify the initial
investment of the proposed system, due to the increase of
number of switches.
2. COMPONENTS INPROPOSED CIRCUIT
2.1 Effect of Source Inductance
In the Fig.1, lg’, la’, lb, lb’ are input side inductors these
inductors are called source inductors. The input side bridge
rectifier is a fully controlled rectifier. The presence of source
inductance introduces an additional mode of operation of
when firing angle is less than certain value.
When there is an inductor in series with each input line, it is
necessary to find out its effect. The effects are
1. The reduction in output voltage
2. The duration of commutation overlap.
3. The relationship between the firing angle and the
commutation overlap.

__________________________________________________________________________________________
Fig 1 Proposed single-phase to three-phase drive system
2.2 DC Link Capacitor
A simple analytical expression for the current stress on the
DC-link capacitor caused by the load-side inverter of a voltage
DC-link-converter system is derived. The DC-link capacitor
current RMS value is determined from the modulation depth
and by the amplitude and the phase angle of the inverter
output current assuming a sinusoidal inverter output current
and a constant DC-link voltage.
Despite neglecting the output-current ripple, the results of the
analytical calculation are within 8% of measurements made
from digital simulation and an experimental system, even if
the output-current ripple is relatively high as in the case of
low-frequency IGBT inverter systems. The simple analytical
expression provides significant advantages over simulation
methods for designing the DC-link capacitor of PWM
converter systems.
2.3 IGBT Fundamentals
The Insulated Gate Bipolar Transistor (IGBT) is a minority-
carrier device with high input impedance and large bipolar
current-carrying capability. Many designers view IGBT as a
device with MOS input characteristics and bipolar output
characteristic that is a voltage-controlled bipolar device. To
make use of the advantages of both Power MOSFET and BJT,
the IGBT has been introduced. It’s a functional integration of
Power MOSFET and BJT devices in monolithic form. It
combines the best attributes of both to achieve optimal device
characteristics.
The IGBT is suitable for many applications in power
electronics, especially in Pulse Width Modulated (PWM)
servo and three-phase drives requiring high dynamic range
control and low noise. It also can be used in Uninterruptible
Power Supplies (UPS), Switched-Mode Power Supplies
(SMPS), and other power circuits requiring high switch
repetition rates. IGBT improves dynamic performance and
efficiency and reduced the level of audible noise. It is equally
suitable in resonant-mode converter circuits. Optimized IGBT
is available for both low conduction loss and low switching
loss.
SCR, the Triac conducts in either direction when turned on.
The Triac also differs from the SCR in that either a positive or
negative gate signal triggers it into conduction. Thus the Triac
is a three terminal, four layer bidirectional semiconductor
device that controls ac power whereas an SCR controls dc
power or forward biased half cycles of ac in a load. Because of
its bidirectional conduction property, the Triac is widely used
in the field of power electronics for
It is wound for a definite number of poles. The windings are
geometrically spaced 120 degrees apart. Two types of rotors
are used in Induction motors Squirrel cage rotor and Wound
rotor.
3. PULSE WIDTHMODULATION
3.1 General Description
The PWM component provides compare outputs to generate
single or continuous timing and control signals in hardware.
The PWM is designed to provide an easy method of
generating complex real-time events accurately with minimal
CPU intervention. PWM features may be combined with other
analog and digital components to create custom peripherals.
The PWM generates up to two left- or right-aligned PWM
outputs or one centered-aligned or dual edged PWM output.
The PWM outputs are double buffered to avoid glitches
caused by duty cycle changes while running. Left-aligned
PWMs are used for most general-purpose PWM uses .Right-
aligned PWMs are typically only used in special cases that
require alignment opposite of left-aligned PWMs. Dual-edged
PWMs are optimized for power conversion where phase
alignment must be adjusted.
The optional dead band provides complementary outputs with
adjustable dead time where both outputs are low between each
transition. The complementary outputs and dead time are most
often used to drive power devices in half-bridge configurations
to avoid shoot-through current sand resulting damage. A kill
input is also available that immediately disables the dead band
outputs when enabled. Three kill modes are available to
support multiple use scenarios. Two hardware dither modes
are provided to increase PWM flexibility. The first dither mo
de increases effective resolution by two bits when resources or
clock frequency preclude a standard implementation in the
PWM counter.

__________________________________________________________________________________________
The second dither mode uses a digital input to select one of the
two PWM outputs on a cycle-by-cycle basis, this mode is
typically used to provide fast transient response in power
converts. The trigger and reset inputs allow the PWM to be
synchronized with other internal or external hardware. The
optional trigger input is configurable so that a rising edge
starts the PWM. A rising edge on the reset input causes the
PWM counter to reset its count as if the terminal count was
reached. The enable input provides hardware enable to gate
PWM operation based on a hardware signal. An interrupt can
be programmed to be generated under any combination of the
following conditions. When the PWM reaches the terminal
count or when a compare output goes high.
The most common use of the PWM is to generate periodic
waveforms with adjustable duty cycles. The PWM also
provides optimized features for power control, motor control,
switching regulators, and lighting control. You can also use
the PWM as a clock divider by driving a clock into the clock
input and using the terminal count or a PWM output as the
divided clock output. PWMs, timers, and counters share many
capabilities, but each provides specific capabilities. A Counter
component is better used in situations that require the counting
of a number of events but also provides rising edge capture
input as well as a compare output.
3.2 Space Vector PWM
The initial use of Space Vector Modulation at three-phase
voltage-source inverters has been expanded by application to
novel three-phase topologies as AC/DC Voltage Source
Converter, AC/DC or DC/AC Current Source Converters,
Resonant Three-Phase Converters, B4-inverter, Multilevel
Converters, AC/AC Matrix Converters, and so on. The Space
Vector PWM generation module accepts modulation index
commands and generates the appropriate gate drive
waveforms for each PWM cycle. This section describes the
operation and configuration of the SVPWM module.
A three-phase 2-level inverter with dc link configuration can
have eight possible switching states, which generates output
voltage of the inverter. Each inverter switching state generates
a voltage Space Vector (V1 to V6 active vectors, V7 and V8
zero voltage vectors) in the Space Vector plane. The
magnitude of each active vector (V1to V6) is 2/3 Vdc (dc bus
voltage).
Fig 2 A three-phase two-level inverter with dc link
configuration
The three-phase inverter presented in Fig 2 is here in
considered. Fig 3 presents the appropriate output voltages
without PWM (six-step).
Fig 3 Output voltage waveforms and state coding for the case
Without PWM
Each state of the output voltage system leads to a switching
vector in the complex plane. It results 6 active switching
vectors V1 …V6 and 2 vectors corresponding to the zero
states. The magnitude of the active vectors is (2/3) Vdc. Since
the output voltages are at 2pi/3 out of phase each other, the
Space Vectors system can occupy a number of positions with
an order multiple of three.
3.3 Principle of Pulse Width Modulation (PWM)
Fig 4 Circuit model of a single-phase inverter with a centre-
taped grounded DC bus
Fig 5 Pulse width modulation

__________________________________________________________________________________________
As depicted in Fig 4 the inverter output voltage is determined
in the following
When V control > V tri, VA0= V dc/2
When V control < V tri, VA0 = V dc/2
Also, the inverter output voltage has the following features
PWM frequency is the same as the frequency of V tri
Amplitude is controlled by the peak value of V control
Fundamental frequency is controlled by the frequency of V
control
4. RECTIFIER AND INVERTER
4.1 AC to DC converter
A rectifier is an electrical device that converts alternating
current (AC), which periodically reverses direction, to direct
current (DC), which is in only one direction, a process known
as rectification. Rectifiers have many uses including as
components of power supplies and as detectors of radio
signals. Rectifiers may be made of solid state diodes, vacuum
tube diodes, mercury arc valves, and other components.
When only one diode is used to rectify AC (by blocking the
negative or positive portion of the waveform), the difference
between the term diode and the term rectifier merely one of
usage, i.e, the term rectifier is describes a diode that is being
used to convert AC to DC.
4.1.1 Half-Wave Rectification
In half wave rectification, either the positive or negative half
of the AC wave is passed, while the other half is blocked.
Because only one half of the input waveform reaches the
output, it is very inefficient if used for power transfer. Half-
wave rectification can be achieved with a single diode in a
one-phase supply, or with three diodes in a three-phase supply.
Fig 6 Half wave rectification
The output DC voltage of a half wave rectifier can be
calculated with the following two ideal equations
Vrms =
Vpeak
2
Vdc =
Vpeak
π
4.1.2 Full-Wave Rectification
A full-wave rectifier converts the whole of the input waveform
to one of constant polarity (positive or negative) at its output.
Full-wave rectification converts both polarities of the input
waveform to DC (direct current), and is more efficient.
However, in a circuit with a non-centre transformer, four
diodes are required instead of the one needed for half-wave
rectification. Four diodes arranged this way are called a diode
bridge or bridge rectifier.
Fig 7 A Full-Wave Rectifier Using Four Diodes
For single-phase AC, if the transformer is centre-tapped, then
two diodes back-to-back (i.e. anodes-to-anode or cathode-to-
cathode) can form a full-wave rectifier. Twice as many
windings are required on the transformer secondary to obtain
the same output voltage compared to the bridge rectifier
above.
Fig 8 Full-wave rectifier using a centre tap transformer and
two diodes
Fig 9 A three-phase bridge rectifier
Three phase AC input

__________________________________________________________________________________________
Three phase half wave rectifier
Three phase full wave rectifier
Fig 10 Three-phase AC input, half and full wave rectified DC
output waveforms
For three-phase AC, six diodes are used. Typically there are
three pairs of diodes, each pair, though, is not the same kind
of double diode that would be used for a full wave single-
phase rectifier. Instead the pairs are in series (anode to
cathode). Typically, commercially available double diodes
have four terminals so the user can configure them as single-
phase split supply use, for half a bridge, or for three-phase
use.Most devices that generate alternating current (such
devices are called alternators) generate three-phase AC. For
example, an automobile alternator has six diodes inside it to
function as a full-wave rectifier for battery charging
applications. The average and root-mean-square output
voltages of an ideal single phase full wave rectifier can be
calculated as
Vdc = Vav =
2Vp
π
Vrms =
Vp
2
Where
Vdc and Vav are the average and DC output voltage.
Vp is the peak value of half wave.
The extreme of this approach is to dispense with the reservoir
capacitor altogether and put the rectified waveform straight
into a choke-input filter. The advantage of this circuit is that
the current waveform is smoother and consequently the
rectifier no longer has to deal with the current as a large
current pulse, but instead the current ctrical device that
converts direct current (DC) to alternating current (AC), the
converted AC can be at any required voltage and frequency
with the use of appropriate transformers, switching, and
control circuits.
Solid-state inverters have no moving parts and are used in a
wide range of applications, from small switching power
supplies in computers, to large electric utility high-voltage
direct current applications that transport bulk power. Inverters
are commonly used to supply AC power from DC sources
such as solar panels or batteries. There are two
main types of inverter. The output of a modified sine
wave inverter is similar to a square wave output except that
the output goes to zero volts for a time before switching
positive or negative. Thus it is compatible with all AC
electronic devices. This is the type used in grid-tie inverters.
Its design is more complex, and costs 5 or 10 times more per
unit power. The electrical inverter is a high-power electronic
oscillator. It is so named because early mechanical AC to DC
converters was made to work in reverse, and thus were
“inverted”, to convert DC to AC. The inverter performs the
opposite function of a rectifier.
5. MODELLING AND CASE STUDY
5.1 System Model
The system is composed of grid, input inductors
(𝐿 𝑎, 𝐿′ 𝑎 , 𝐿 𝑏 , 𝐿′ 𝑏 ). Rectifiers (A and B), capacitor bank at the
dc-link, inverter, and induction machine Rectifiers A and B
are constituted of switches 𝑞 𝑎1 , 𝑞 𝑎1, 𝑞 𝑎2 and 𝑞 𝑎2 and
𝑞 𝑏1 , 𝑞 𝑏1, 𝑞 𝑏2 and 𝑞 𝑏2respectively. The inverter is constituted of
switches𝑞𝑠1 , 𝑞𝑠1, 𝑞𝑠2, 𝑞𝑠2, 𝑞𝑠3and𝑞𝑠3.
From Fig.12, the following equations can be derived for the
front-end rectifier
𝑣 𝑎10 − 𝑣 𝑎20 = 𝑒 𝑔 − 𝑟𝑎 + 𝑙 𝑎 𝑝 𝑖 𝑎 − ( 𝑟′ 𝑎 + 𝑙′ 𝑎 𝑝 )𝑖′ 𝑎 (1)
𝑣 𝑏10 − 𝑣 𝑏20 = 𝑒 𝑔 − 𝑟𝑏 + 𝑙 𝑏 𝑝 𝑖 𝑏 − ( 𝑟′ 𝑏 + 𝑙′ 𝑏 𝑝 )𝑖′ 𝑏 (2)
𝑣 𝑎10 − 𝑣 𝑏10 = 𝑟𝑏 + 𝑙 𝑏 𝑝 𝑖 𝑏 − ( 𝑟𝑎 + 𝑙 𝑎 𝑝 )𝑖 𝑎 (3)
𝑣 𝑎20 − 𝑣 𝑏20 = 𝑟′ 𝑎 + 𝑙′ 𝑎 𝑝 𝑖′ 𝑎 − ( 𝑟′ 𝑏 + 𝑙′ 𝑏 𝑝 )𝑖′ 𝑏 (4)
𝑖 𝑔 = 𝑖 𝑎 + 𝑖 𝑏 = 𝑖′ 𝑎 + 𝑖′ 𝑏 (5)
Where p = d/dt and symbols like r and l represent the
resistances and inductances of the input
inductors𝐿 𝑎 , 𝐿′ 𝑎 , 𝐿 𝑏 , 𝐿′ 𝑏 .
The circulating current 𝑖0 can be defined from𝑖 𝑎 , 𝑖′ 𝑎 𝑖 𝑏, 𝑖′ 𝑏 .
𝑖0 = 𝑖 𝑎 − 𝑖′ 𝑎 = −𝑖 𝑏 + 𝑖′ 𝑏 (6)
Introducing 𝑖0and adding (3) and (4), relations (1)–(4) Become

__________________________________________________________________________________________
𝑣𝑎 = 𝑒 𝑔 − [ 𝑟𝑎 + 𝑟′
𝑎 +(𝑙 𝑎 + 𝑙′
𝑎)𝑝]𝑖 𝑎 + ( 𝑟′
𝑎 + 𝑙′ 𝑎 𝑝 )𝑖0
(7)
𝑣 𝑏 = 𝑒 𝑔 − [ 𝑟𝑏 + 𝑟′
𝑏 +(𝑙 𝑏 + 𝑙′
𝑏 )𝑝]𝑖 𝑏 + ( 𝑟′
𝑏 + 𝑙′ 𝑏 𝑝 )𝑖0
(8)
𝑣0 = −[ 𝑟′
𝑎 + 𝑟′
𝑏 +(𝑙 𝑏 + 𝑙′
𝑏 )𝑝]𝑖0
− [ 𝑟𝑎 − 𝑟′
𝑎 +(𝑙 𝑎 − 𝑙′
𝑎)𝑝]𝑖 𝑎 +
[ 𝑟𝑏 − 𝑟′
𝑏 +(𝑙 𝑏 + 𝑙′
𝑏 )𝑝]𝑖 𝑏 (9)
Where
𝑣𝑎 = 𝑣 𝑎10 − 𝑣 𝑎20 (10)
𝑣 𝑏 = 𝑣 𝑏10 − 𝑣 𝑏20 (11)
𝑣𝑎 = 𝑣 𝑎10 + 𝑣 𝑎20 − 𝑣 𝑏10 − 𝑣 𝑏20 (12)
Relations (7)–(9) and (5) constitute the front-end rectifier
dynamic model. Therefore, 𝑣𝑎 (rectifier A), 𝑣 𝑏 (rectifier B), and
𝑣0(rectifiers A and B) are used to regulate currents 𝑖 𝑎 , 𝑖 𝑏 , 𝑖0
respectively. Reference currents 𝑖 𝑎
∗
and 𝑖 𝑏
∗
are chosen equal to
𝑖 𝑔
∗
2 and the reference circulating current 𝑖0
∗
is chosen equal to
0.
Fig 11 Single-phase to three-phase drive system
In order to both facilitate the control and share equally current,
voltage, and power between the rectifiers, the four inductors
should be equal, i.e.𝑟′
𝑔 = 𝑟𝑎 = 𝑟′
𝑎 = 𝑟𝑏 = 𝑟′
𝑏 and 𝑙′ 𝑔 = 𝑙 𝑎 =
𝑙′ 𝑎 = 𝑙 𝑏 = 𝑙′ 𝑏 . In this case, the model (7)–(9) can be simplified
to the model given by
𝑣𝑎 +
𝑣0
2
= 𝑒 𝑔 − 2 𝑟′ 𝑔 + 𝑙′ 𝑔 𝑝 𝑖 𝑎 (13)
𝑣𝑎 −
𝑣0
2
= 𝑒 𝑔 − 2 𝑟′ 𝑔 + 𝑙′ 𝑔 𝑝 𝑖 𝑏 (14)
𝑣0=−2 𝑟′ 𝑔 + 𝑙′ 𝑔 𝑝 𝑖0 (15)
Additionally, the equations for𝑖 𝑔,𝑖′ 𝑎 and 𝑖′ 𝑏 can be written as
𝑣 𝑎𝑏 =
𝑣 𝑎 + 𝑣 𝑏
2
=𝑒 𝑔 − 𝑟′ 𝑔 + 𝑙′ 𝑔 𝑝 𝑖 𝑔 (16)
𝑣𝑎 −
𝑣0
2
= 𝑒 𝑔 − 2 𝑟′ 𝑔 + 𝑙′ 𝑔 𝑝 𝑖′ 𝑎 (17)
𝑣𝑎 +
𝑣0
2
= 𝑒 𝑔 − 2 𝑟′ 𝑔 + 𝑙′ 𝑔 𝑝 𝑖′ 𝑏 (18)
In this ideal case (four identical inductors), the circulating
current can be reduced to zero imposing.
𝑣0 = 𝑣 𝑎10 + 𝑣 𝑎20 − 𝑣 𝑏10 − 𝑣 𝑏20=0 (19)
When 𝑖0=0 (𝑖 𝑎 = 𝑖′ 𝑎 , 𝑖 𝑏 = 𝑖′ 𝑏 ) the system model (7)–(9) is
reduced to
𝑣𝑎 = 𝑒 𝑔 −2(𝑟𝑔
′
+𝑙 𝑔
′
𝑝)𝑖 𝑎 (20)
𝑣 𝑏 = 𝑒 𝑔 −2(𝑟𝑔
′
+𝑙 𝑔
′
𝑝)𝑖 𝑏 (21)
Fig 12 Proposed single-phase to three-phase drive system
5.2 PWM Strategy
The PWM strategy for the rectifier will be presented. The
rectifier pole voltages 𝑣 𝑎10, 𝑣 𝑎20, 𝑣 𝑏10and 𝑣 𝑏20depend on the
conduction states of the power switches, i.e.
𝑣𝑗0= (2𝑠 𝑞𝑗 -1)
𝑣 𝑐
2
, for j=a1 to b2 (22)
Where 𝑣𝑐 is the total dc-link voltage. Considering that𝑣𝑎
∗
,𝑣 𝑏
∗
and 𝑣0
∗
denote the reference voltages determined by the current
controllers.
𝑣𝑎
∗
= 𝑣 𝑎10
∗
− 𝑣 𝑎20
∗
(23)
𝑣 𝑏
∗
= 𝑣 𝑏10
∗
− 𝑣 𝑏20
∗
(24)
𝑣0
∗
= 𝑣 𝑎10
∗
+ 𝑣 𝑎20
∗
− 𝑣 𝑏10
∗
− 𝑣 𝑏20
∗
(25)

__________________________________________________________________________________________
The gating signals are directly calculated from the reference
pole voltages𝑣 𝑎10
∗
, 𝑣 𝑎20
∗
, 𝑣 𝑏10
∗
and 𝑣 𝑏20
∗
. However, (23)–(25) are
not sufficient to determine the four pole voltages uniquely
from𝑣𝑎
∗
,𝑣 𝑏
∗
and𝑣0
∗
. Introducing an auxiliary variable 𝑣𝑥
∗
=𝑣 𝑎20
∗
,
that equation plus the three equations (23)–(25) constitute a
four independent equations system with four variables
(𝑣 𝑎10
∗
, 𝑣 𝑎20
∗
, 𝑣 𝑏10
∗
and𝑣 𝑏20
∗
). Solving this system of equations,
we obtain
𝑣 𝑎10
∗
=𝑣𝑎
∗
+ 𝑣𝑥
∗
(26)
𝑣 𝑎20
∗
= 𝑣𝑥
∗
(27)
𝑣 𝑏10
∗
=
𝑣 𝑎
∗
2
+
𝑣 𝑏
∗
2
−
𝑣0
∗
2
+ 𝑣𝑥
∗
(28)
𝑣 𝑏20
∗
=
𝑣 𝑎
∗
2
−
𝑣 𝑏
∗
2
−
𝑣0
∗
2
+ 𝑣𝑥
∗
(29)
From these equations, it can be seen that, besides𝑣𝑎
∗
,𝑣 𝑏
∗
and𝑣0
∗
,
the pole voltages depend on also of𝑣𝑥
∗
. The limit values of the
variable 𝑣𝑥
∗
can be calculated by taking into account the
maximum 𝑣𝑐
∗
2 and minimum –𝑣𝑐
∗
2 value of the pole
voltages.
𝑣𝑥𝑚𝑎𝑥
∗
=
𝑣 𝑐
∗
2
− 𝑣 𝑚𝑎𝑥
∗
(30)
𝑣 𝑥𝑚𝑖𝑛
∗
=
𝑣 𝑐
∗
2
− 𝑣 𝑚𝑖𝑛
∗
(31)
Where 𝑣𝑐
∗
is the reference dc-link voltages, 𝑣 𝑚𝑎𝑥
∗
= max ϑ
and𝑣 𝑚𝑖𝑛
∗
= minϑ, with ϑ= { 𝑣𝑎
∗
, 0, 𝑣𝑎
∗
2 + 𝑣 𝑏
∗
2 −
𝑣0
∗
2 , 𝑣𝑎
∗
2 − 𝑣 𝑏
∗
2 − 𝑣0
∗
2}.
Introducing a parameter μ (0 ≤ μ ≤ 1), the variable𝑣𝑥
∗
can be
written as
𝑣𝑥
∗
= 𝜇𝑣𝑥𝑚𝑎𝑥
∗
+ (1 − 𝜇)𝑣 𝑥𝑚𝑖𝑛
∗
(32)
When μ = 0, μ = 0.5, and μ = 1 the auxiliary variable 𝑣𝑥
∗
Has
the following values 𝑣𝑥
∗
= 𝑣 𝑥𝑚𝑖𝑛
∗
, 𝑣𝑥
∗
= 𝑣𝑥𝑎𝑣𝑒
∗
= (𝑣 𝑥𝑚𝑖𝑛
∗
+𝑣𝑥𝑚𝑎𝑥
∗
)/2and 𝑣𝑥
∗
= 𝑣𝑥𝑚𝑎𝑥
∗
, respectively. When 𝑣𝑥
∗
∗
or
𝑣𝑥
∗
∗
a converter leg operates with zero switching
frequency. The gating signals are obtained by comparing pole
voltages with one (𝑣𝑡1 ), two (𝑣𝑡1and𝑣𝑡2) or more high-
frequency triangular carrier signals. In the case of double-
carrier approach, the phase shift of the two triangular carrier
signals (𝑣𝑡1and𝑣𝑡2) is1800
.The parameter μ changes the place
of the voltage pulses related to 𝑣𝑎 and 𝑣 𝑏 . When 𝑣𝑥
∗
∗
(μ
= 0) or 𝑣𝑥
∗
∗
(μ = 1) are selected, the pulses are placed in
the begin or in the end of the half period (Ts ) of the triangular
carrier signal On the other hand, when 𝑣𝑥
∗
=𝑣𝑥𝑎𝑣𝑒
∗
the pulsesare
centered in the half period of the carrier signal.
The change of the position of the voltage pulses leads also to
the change in the distribution of the zero instantaneous
voltages (i.e., 𝑣𝑎 = 0 and 𝑣 𝑏 = 0).With μ = 0 or μ = 1 the zero
instantaneous voltages are placed at the beginning or at the
end of the switching period, respectively, while with μ = 0.5,
they are distributed equally at the beginning and at the end of
the half period. This is similar to the distribution of the zero-
voltage vector in the three-phase inverter.
5.3 Control Strategy
Fig.13 presents the control block diagram of the system in Fig.
12. highlighting the control of the rectifier, to control the dc-
link voltage and to guarantee the grid power factor close to
one. Additionally, the circulating current 𝑖0in the rectifier of
the proposed system needs to be controlled.
Fig.13 Control block diagram
In this way, the dc-link voltage 𝑣𝑐is adjusted to its reference
value 𝑣𝑐
∗
using the controller 𝑅 𝑐.which is standard Fuzzy logic
controllers. This controller provides the amplitude of the
reference grid current 𝑖 𝑔
∗
To control power factor and
harmonics in the grid side, the instantaneous reference current
𝑖 𝑔
∗
must be synchronized with voltage 𝑒 𝑔, as given in the
voltage-oriented control (VOC) for three-phase system This is
obtained via blocks Ge-𝑖 𝑔, based on a PLL scheme. The
reference currents 𝑖 𝑎
∗
and 𝑖 𝑏
∗
are obtained by making
𝑖 𝑎
∗
=𝑖 𝑏
∗
=𝑖 𝑔
∗
2.Which means that each rectifier receives half of
the grid current. The control of the rectifier currents is
implemented using the controllers indicated by blocks
𝑅 𝑎and𝑅 𝑏 . These controllers can be implemented using linear
or nonlinear techniques.
The homo polar current is measured (𝑖0) and compared to its
reference (𝑖0
∗
= 0). The error is the input of Fuzzy controller
𝑅0that determines the voltage 𝑣0
∗
. The calculation of voltage
𝑣𝑥
∗
isgiven from (30) to (32) as a function of μ, selected. The

__________________________________________________________________________________________
motor there phase voltages are supplied from the inverter
(VSI).
Block VSI-Ctr indicates the inverter and its control. The
control system is composed of the PWM command and a
torque or flux control strategy.
5.4 Harmonic Distortion
The harmonic distortion of the converter voltages has been
evaluated by using the weighted THD (WTHD). It is
computed by using
𝑊𝑇𝐻𝐷(𝑝) =
100
𝑎1
𝑎 𝑖
𝑖
2
𝑝
𝑖=2 (33)
Where 𝑎1the amplitude of the fundamental voltage is is 𝑎𝑖is
the amplitude of ith harmonic and p is the number of
harmonics taken into consideration. Fig.5.4. shows the WTHD
of voltages generated by rectifiers𝑣 𝑎𝑏 = (𝑣𝑎 + 𝑣 𝑏 ) 2 for the
proposed configuration and 𝑣𝑔 = 𝑣 𝑔10 − 𝑣 𝑔20 for the
conventional one] at rated grid voltage asa function of μ. Note
that the parameter μ determines 𝑣𝑥
∗
from (30) to (32). The
resultant voltage 𝑣 𝑎𝑏 generated by rectifieris responsible to
control 𝑖 𝑔, which means that this voltage is used to regulate the
harmonic distortion of the utility grid.
Fig 14 WTHD of rectifier voltage as a function of μ.
When the single-carrier PWM is used, the behavior of WTHD
of the proposed system is similar to that of conventional one
for all μ, as observed in Fig.5.4. When the double-carrier
PWM is used with μ = 0.5, the WTHD is also the same for
both configurations. However, for the other values of μ the
WTHD of the proposed system is lower than that of the
conventional one.
The WTHD of the proposed topology (double-carrier with μ =
0or μ = 1) is close to 63% of that of the conventional
topology(with μ = 0.5). The study has also shown that it is
possible to reduce the switching frequency of the proposed
system in 60%and still have the same WTHD of the standard
configuration.
Fig. 15 Variables of rectifiers A and B. (a) Single-carrier with
μ = 1.
(b) Single-carrier with μ = 0.5. (c) Double-carrier with μ = 1.
(d) Double carrier with μ =0.5.
The WTHD behavior in Fig. 14 can be explained from Fig.
15.That figure depicts the pole voltages (𝑣 𝑎10, 𝑣 𝑎20 , 𝑣 𝑏10,𝑣 𝑏20)
and their references (𝑣 𝑎10
∗
, 𝑣 𝑎20
∗
, 𝑣 𝑏10
∗
,𝑣 𝑏20
∗
), the triangular
carrier signals (𝑣𝑡1, 𝑣𝑡2 ), the resultant rectifier voltage (𝑣 𝑎𝑏 )
and the circulating voltage (𝑣0). Fig 15 (a) and (c) shows these
variables with single-carrier (with μ = 1) and double-carrier
(with μ = 1), respectively.
For the double-carrier see Fig. 15 (c) the voltage 𝑣 𝑎𝑏 has
smaller amplitude and better distribution along the half
switching period than that of single-carrier see Fig. 15
(a),which means a lower WTHD(as observed in Fig. 4 for μ =
1).
On the other hand, for μ = 0.5 see Fig. 15 (b) and (d) the
distribution of voltage 𝑣 𝑎𝑏 along the switching period is the
same for both cases, i.e., single-carrier and double-carrier have
the same WTHD. Besides the total harmonic distortion (THD)
of the grid current𝑖 𝑔, associated to the WTHD of the
voltage𝑣 𝑎𝑏 , the harmonic distortion analysis must also
consider the currents in the rectifiers. This is an important
issue due to losses of the converter.
The harmonic distortion of the rectifier current (𝑖 𝑎 , 𝑖′ 𝑎 , 𝑖 𝑏 , 𝑖′ 𝑏 )
with double-carrier is higher than that of the grid current ig .
When the parallel rectifier with double-carrier is used, the
THD of all these currents are reduced for μ = 0 or μ = 1 and
increased for μ = 0.5. On the other hand, the THD of the
circulating current is also smaller with μ = 0 or μ = 1. Fig. 16

__________________________________________________________________________________________
shows currents 𝑖 𝑎 , 𝑖′ 𝑎 , 𝑎𝑛𝑑 𝑖0for double-carrier with μ = 1 and
μ = 0.5. It can be seen that the mean values of the ripples of all
currents are smaller when μ = 1 is selected..
Fig 16 currents 𝑖 𝑎 , 𝑖′ 𝑎 , 𝑎𝑛𝑑 𝑖0for double-carrier with μ
= 1 and μ = 0.5
In conclusion the optimal rectifier operation is obtained with
double-carrier making μ = 0 or μ = 1. A four-carrier approach
may also be used.
5.5 Ratings of Switches
Assuming same rms voltages at both grid and machine sides ,a
machine power factor of 0.85 and neglecting the converter
losses, currents of the rectifier switches normalized in terms of
currents of the inverter switches are 2.55 and 1.27 for the
conventional and the proposed single-phase to three-phase
converter, respectively. Fig (a) and (b) shows the flow of
active power in the conventional and in the proposed single-
phase to three-phase converter, respectively. For balanced
system (𝐿′ 𝑔 = 𝐿 𝑎 = 𝐿′ 𝑎 = 𝐿 𝑏 = 𝐿′ 𝑏 ), voltage 𝑣0is close to
zero, so that the dc-link voltage is equal to that required by the
conventional system. Since the parallel connection scheme
permits to reduce the switch currents and preserve the dc-link
voltage, the rating of each power switch in the rectifier side is
reduced.
6. SIMULATION MODELING AND RESULTS
6.1 Simulation Modeling for Transient Condition
In this chapter the work carried out on mathematical model of
the system using MATLAB/SIMULINK software. The results
of simulation have been discussed.
Fig 17 Simulation model of single phase to three phase drive
system using two parallel single phase rectifiers
Fig 18 (a) Control Block Diagram

__________________________________________________________________________________________
Fig 18 (b) Space Vector PWM Diagram
6.2 Simulation Results for Transient Condition
Fig 19(a) Grid voltage and current
Fig 19(b) Capacitor voltage
Fig 19(c) Currents of rectifier A ( ia and ia’) and circulating
current
Fig 19(d) Currents of rectifier A (ia) and rectifier B current
(ib)
Fig 19(e) Line to line voltage of load
6.3 Simulation Modeling Faulty Zone at Rectifier
Fig20 Fault Identified at rectifier B
6.3.1 Simulation results for fault at rectifier B

__________________________________________________________________________________________
Fig 21(a) Grid voltage and grid current
Fig 21(b) DC link capacitor voltage
Fig 21(c) Currents of rectifier A and B
Fig 21 (d) Currents of rectifier (ia and ia’)
6.3.2 Output Wave Form Explanation for Transient
Condition.
1. Figure 19(a) represents grid voltage and current at
transient condition. grid voltage is 110V,grid current
is 8A. At the transient condition grid current having
some distortions, after some it will reaches to steady
state condition. Time taken for steady state is 0.25 m
sec.
2. Figure 19(b) represents the DC link Capacitor
voltage. At steady state capacitor value is 100V.
3. Figure 19(c) represents rectifier A currents ia and ia’.
The current shared by rectifier A is 4A. it is the half
of grid current. Circulating current is represented.
4. Figure 19(d) represents rectifier A current and
rectifier B currents at transient condition. When it
reaches to steady state value the currents of rectifier
A and B is 4A.
5. Figure 19(e) represents line to line voltage of load. At
transient condition it is low value. At steady state line
voltage of load is 125V.
6.3.3 Output Wave Form Explanation for Fault At
Rectifier B
1. Figure 21(a) represents grid voltage and currents.
From the figure up to 0.2 m sec rectifier A and B is in
healthy condition then current sharing is equal. When
fault occurred in rectifier B the total grid current 8A
is shared by Rectifier A.
2. Figure 21(b) represents the capacitor voltage. The
capacitor voltage 100V. when fault occurred rectifier
B capacitor voltage decreases and again it reaches to
100V.
3. Figure 21(c) represents the rectifiers currents when
fault at rectifier B. The total grid current is shared by
rectifier A is started at 0.5m sec.
4. Figure 21(d) represents rectifier currents ia and ia’.
The current magnitude of these two currents is
CONCLUSIONS
A single-phase to three-phase drive system composed of two
parallel single-phase rectifiers, a three-phase inverter and an
induction motor was proposed. The system combines two
parallel rectifiers without the use of transformers. The system
model and the control strategy, including the PWM technique,
have been developed.
The complete comparison between the proposed and standard
configurations has been carried out in this paper. Compared to
the conventional topology, the proposed system permits to
reduce the rectifier switch currents, the THD of the grid
current with same switching frequency or the switching
frequency with same THD of the grid current and to increase
the fault tolerance characteristics. In addition, the losses of the
proposed system may be lower than that of the conventional
counterpart.
The initial investment of the proposed system (due to high
number of semiconductor devices) cannot be considered a
drawback, especially considering the scenario where the cited
advantages justify such initial investment. The experimental
results have shown that the system is controlled properly, even
with transient and occurrence of fault
FUTURE SCOPE
It is quite common to have only a single phase power grid in
residential, commercial, manufacturing, and mainly in rural
areas. At the solar power plant and industries it is convenient
convert single phase supply to three phase supply. This system
is very useful for agricultural to run three phase motor.
REFERENCES
[1] D.-C. Lee and Y.-S. Kim, “Control of single-phase-to-
three-phase AC/DC/AC PWM converters for induction

__________________________________________________________________________________________
motor drives,” IEEE Trans. Ind. Electron., vol. 54, no. 2,
pp. 797–804, Apr. 2007.
[2] D. J. Nowak, A. Bendre, G. Oriti, and A. L. Julian,
“Mitigating circulating common-mode currents between
parallel soft-switched drive systems,” IEEE Trans. Ind.
Appl., vol. 43, no. 5, pp. 1284–1294,. R. M. Cuzner,
Sep./Oct. 2007.
[3] C. B. Jacobina, E. C. dos Santos Jr., E. R. C. da Silva, M.
B. R. Correa, A. M. N. Lima, and T. M. Oliveira,
“Reduced switch count multiple three phase ac machine
drive systems,” IEEE Trans. Power Electron., vol. 23,
no. 2, pp. 966–976,
[4] Z. Ye, P. Jain, and P. Sen, “Circulating current
minimization in high frequency AC power distribution
architecture with multiple inverter modules operated in
parallel,” IEEE Trans. Ind. Electron., vol. 54, no. 5, pp.
2673–2687, Oct. 2007.
[5] P.-T. Cheng, C.-C. Hou, and J.-S. Li, “Design of an
auxiliary converter for the diode rectifier and the analysis
of the circulating current,” IEEE Trans. Power Electron.,
vol. 23, no. 4, pp. 1658–1667, Jul. 2008.
[6] H. Cai, R. Zhao, and H. Yang, “Study on ideal operation
status of parallel inverters,” IEEE Trans. Power
Electron., vol. 23, no. 6, pp. 2964–2969, Nov. 2008.
[7] J. Holtz, “Pulse width modulation for electronic power
conversion,” Proc.

Two parallel single phase rectifiers by using single phase to three phase induction motor

More Related Content

What's hot

Similar to Two parallel single phase rectifiers by using single phase to three phase induction motor

More from eSAT Journals

Recently uploaded

Two parallel single phase rectifiers by using single phase to three phase induction motor